Motivated by the functional structure of the so-called weighted Morrey spaces [1]}, in Diagana [2]}, a new concept called
doubly-weighted pseudo-almost periodicity, which generalizes in a natural fashion the notion of weighted pseudo-almost periodicity is introduced and studied.
Among other things, in [2]}, properties of these new functions have been studied including the stability of the convolution operator, the translation-invariance, the existence of a doubly-weighted mean for almost periodic functions under some reasonable assumptions, the uniqueness of the decomposition involving these new functions as well as some results on the composition of these new functions have been studied.
